Can someone explain to me (a non American) which niche or segment was Spirit in (and perhaps why they, and not any other airline, are shutting shop)?

Low cost carrier. Think Ryanair. Competition from the rest of the market and bad management put them in a bad position, with the most recent war causing unsustainable fuel issues. Other airlines may be able to double/triple their prices in the short term. Spirit's customers may simply choose to not fly.

https://www.npr.org/2026/05/02/nx-s1-5807933/spirit-airlines... describes this in more detail.

Similar to Ryanair in Europe